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Fombitz answered: 13805 problems
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Expressions-with-variables/314830: Seven more than twice Seth's age.
1 solutions

Answer 225177 by Fombitz(13828) About Me  on 2010-06-16 10:06:14 (Show Source):
You can put this solution on YOUR website!
Your problem setup seems to have been cut off.
Please re-post.


logarithm/314762: Express as a single logarithm, and, if possible, simplify.
1/4loga x+8loga y-2loga x
My choices are:
A. Loga x7/4y4
B. Loga 1/7x4y4
C. Loga 7/x4/y4
D. Loga y8/7/x4
I picked D. Is this correct?

1 solutions

Answer 225176 by Fombitz(13828) About Me  on 2010-06-16 10:05:29 (Show Source):
You can put this solution on YOUR website!






.
.
.
I'm not sure which of your answers, this answer corresponds to.


Square-cubic-other-roots/314816: Square root of (x+6)+ square root of (2-6)=4
1 solutions

Answer 225175 by Fombitz(13828) About Me  on 2010-06-16 10:00:48 (Show Source):
You can put this solution on YOUR website!
Check your 2nd expression "sqrt%282-6%29" and re-post your equation.


logarithm/314862: i need the answers to these following questions.
what is the solution of the equation? 30/(1+6e^(-5x))=10
ln(x^2+3x)- ln 10=0
2lnx+ln3
e^(ln2.5)
1 solutions

Answer 225174 by Fombitz(13828) About Me  on 2010-06-16 09:58:25 (Show Source):
You can put this solution on YOUR website!
Only the first two are equations so only those can be solved.
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.
.
30%2F%281%2B6e%5E%28-5x%29%29=10+
30=10%281%2B6e%5E%28-5x%29%29
1%2B6e%5E%28-5x%29=3
6e%5E%28-5x%29=2
e%5E%28-5x%29=2%2F6=1%2F3
-5x=ln%281%2F3%29
highlight%28x=-ln%281%2F3%29%2F5%29
.
.
.
ln%28x%5E2%2B3x%29-ln%2810%29=0+
ln%28x%5E2%2B3x%29=ln%2810%29
x%5E2%2B3x=10
x%5E2%2B3x-10=0
%28x%2B5%29%28x-2%29=0
Two solutions:
x%2B5=0
highlight%28+x=-5%29
.
.
.
x-2=0
highlight%28+x=2%29
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.
.
Please re-post the other two if you still need help with them.



test/314819: In the circle below, angle a = 7x + 2 and angle b = 9x - 4. Find the value of x
1 solutions

Answer 225172 by Fombitz(13828) About Me  on 2010-06-16 09:44:55 (Show Source):
You can put this solution on YOUR website!
No diagram found with a circle.
Please re-post with more information.


Equations/314808: 1/6x+4/3=1/2x+7/3
1 solutions

Answer 225171 by Fombitz(13828) About Me  on 2010-06-16 09:43:13 (Show Source):
You can put this solution on YOUR website!
%281%2F6%29x%2B%284%2F3%29=%281%2F2%29x%2B%287%2F3%29
Multiply both sides by 6 to eliminate fractions.
x%2B8=3x%2B14
-2x=6
highlight%28x=-3%29


Inequalities/314795: solve by elimination
6x=46+4y
5x+-34-7y
1 solutions

Answer 225170 by Fombitz(13828) About Me  on 2010-06-16 09:40:32 (Show Source):
You can put this solution on YOUR website!
You need to re-write the second equation.
It's missing an "=".
Please re-post.


Linear-equations/314786: write the equation of the horizontal line that passes through the point (-1,4)
1 solutions

Answer 225169 by Fombitz(13828) About Me  on 2010-06-16 09:39:17 (Show Source):
You can put this solution on YOUR website!
Horizontal means the slope equals zero.
Use the point-slope form of a line,
y-yp=m%28x-xp%29
y-4=0%28x-1%29
y-4=0
highlight%28y=4%29
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.
.


Linear-equations/314784: Write an equation of the line that passes through the point (2,-3) and is perpendicular to the line given by the equation 3x=4y+5. Give both the point-slope form as well as the slope-intercept form of the answer
1 solutions

Answer 225167 by Fombitz(13828) About Me  on 2010-06-16 09:34:30 (Show Source):
You can put this solution on YOUR website!
3x=4y%2B5
4y=3x-5
y=+%283%2F4%29x-5%2F4
Perpendicular lines have slopes that are negative reciprocals.
m1%2Am2=-1
%283%2F4%29%2Am2=-1
m2=-4%2F3
Use the point-slope form of a line,
+y-yp=m%28x-xp%29
y-%28-3%29=-%284%2F3%29%28x-2%29
highlight_green%28+y%2B3=-%284%2F3%29%28x-2%29%29
Convert to slope-intercept form, y=mx%2Bb
y%2B3=-%284%2F3%29x%2B8%2F3
y=-%284%2F3%29x%2B8%2F3-9%2F3}
highlight_green%28+y=+-%284%2F3%29x-1%2F3+%29


Rational-functions/314772: Hi, I have a few questions I'm having an extremely hard time figuring this out.
1. Find the vertex and intercepts of the parabola y=-3x^2+6
2. Solve the inequality, state the solution using the interval notation and graph it. x-3/x+5<0.
These are both for Math 209. Thank you so much for your time and help.
1 solutions

Answer 225166 by Fombitz(13828) About Me  on 2010-06-16 09:28:07 (Show Source):
You can put this solution on YOUR website!
The parabola is already in vertex form,
y=a%28x-h%29%5E2%2Bk
where (h,k) is the vertex.
It's just a bit hidden.
y=-3x%5E2%2B6
y=-3%28x-0%29%5E2%2B6
The vertex is (0,6).
+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+10%2C+-3x%5E2%2B6%29+
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.
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x-3/x+5<0.
Break up the number line into 3 regions.
Region 1: (-infinity,-5)
Region 2: (-5,3)
Region 3: (3,infinity)
For each region, choose a point (not an endpoint) and test the inequality.
If the inequality is solved, that region is part of the solution.
.
.
.
Region 1: x=-10
%28x-3%29%2F%28x%2B5%29%3C0
%28-10-3%29%2F%28-10%2B5%29%3C0
%28-13%29%2F%28-5%29%3C0
13%2F5%3C0
False, this region is not part of the solution.
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.
.
Region 2: x=0
%28x-3%29%2F%28x%2B5%29%3C0
%280-3%29%2F%280%2B5%29%3C0
-3%2F5%3C0
True, this region is part of the solution.
.
.
.
Region 3: x=5
%28x-3%29%2F%28x%2B5%29%3C0
%285-3%29%2F%285%2B5%29%3C0
2%2F10%3C0
False, this region is not part of the solution.
.
.
.
Only Region 2 is the solution region.
(-5,3)
.
.
.

.
.
.
The curve is below the x-axis(< 0) on in the region (-5,3).


Graphs/314857: how do you graph this equation:
y=50x+150
1 solutions

Answer 225165 by Fombitz(13828) About Me  on 2010-06-16 09:16:48 (Show Source):
You can put this solution on YOUR website!
When x=0, y=50%280%29%2B150=150:(0,150)
When x=-3, y=50%28-3%29%2B150=0:(-3,0)
You now have two points, plot them and connect them with a line.


Problems-with-consecutive-odd-even-integers/314852: How many numbers from 1 to 200 inclusive are equal to the cube of an integer?

1 solutions

Answer 225164 by Fombitz(13828) About Me  on 2010-06-16 09:12:05 (Show Source):
You can put this solution on YOUR website!
1%5E3=1
2%5E3=8
3%5E3=27
4%5E3=64
5%5E3=125
6%5E3=216
So from 1 to 200 there are 5 perfect cubes.


logarithm/314856: log[2 · x]=2.5
I know the answer is 158.11 but i don't know the steps.
1 solutions

Answer 225163 by Fombitz(13828) About Me  on 2010-06-16 09:07:47 (Show Source):


Mixture_Word_Problems/314801: how many gallons of a 40% antifreeze solution and a 70% antifreeze solution must be mixed to get 24 gallons of a 50% antifreeze solution?
1 solutions

Answer 225140 by Fombitz(13828) About Me  on 2010-06-15 23:21:09 (Show Source):
You can put this solution on YOUR website!
1.40X%2B70Y=50%2824%29
2.X%2BY=24
Multiply eq. by -40 and add to eq. 1,
40X%2B70Y-40X-40Y=1200-960
30Y=240
Y=8
Then from eq. 2,
X%2B8=24
X=16
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16 gallons of 40% solution and 8 gallons of 70% solution.


Sequences-and-series/314774: find the sum of the first five terms of the geometric sequence a=12, r=4
1 solutions

Answer 225139 by Fombitz(13828) About Me  on 2010-06-15 23:16:57 (Show Source):


Linear-equations/314780: Write the equation of the horizontal line that passes through (-1,4)
1 solutions

Answer 225138 by Fombitz(13828) About Me  on 2010-06-15 23:13:56 (Show Source):


Equations/314810: Please help me with the answer to this question f(x)=9x+5,g(x)=7x-8
find (fg)(x) thank you
1 solutions

Answer 225137 by Fombitz(13828) About Me  on 2010-06-15 23:13:23 (Show Source):


test/314766: identify all rational zeros of the polynomial function f(x)=3x^4-5x^3-29x^2+45x+18
1 solutions

Answer 225136 by Fombitz(13828) About Me  on 2010-06-15 23:11:04 (Show Source):
You can put this solution on YOUR website!
+graph%28+300%2C300%2C+-5%2C+5%2C+-10%2C+10%2C+3x%5E4-5x%5E3-29x%5E2%2B45x%2B18%29+
Looks like zeros ar x=-3,2,3
Verify using the polynomial,
+3%28-3%29%5E4-5%28-3%29%5E3-29%28-3%29%5E2%2B45%28-3%29%2B18=243%2B135-261-135%2B18=0+
3%282%29%5E4-5%282%29%5E3-29%282%29%5E2%2B45%282%29%2B18=48-40-116%2B90%2B18=0
3%283%29%5E4-5%283%29%5E3-29%283%29%5E2%2B45%283%29%2B18=243-135-261%2B135%2B18=0
.
.
.
+graph%28+300%2C300%2C+-2%2C+1%2C+-10%2C+10%2C+3x%5E4-5x%5E3-29x%5E2%2B45x%2B18%29+
A closer look reveal x=-1/3 as a possible root.

The four roots are then x=-3,-1%2F3,2,3


Linear-systems/314765: y=a and x=b , a and b are real numbers. Is this dependent or independent? consostent or inconsistent? WHY
1 solutions

Answer 225134 by Fombitz(13828) About Me  on 2010-06-15 22:59:13 (Show Source):
You can put this solution on YOUR website!
They are independent and consistent since they are perpendicular to each other.
There is one intersection point at (b,a).


Trigonometry-basics/314751: A ship is traveling at a abearing of 60 degrees for 3 miles then turns and travels at a bearaing of 150 degres for 2 miles then returns to where it started. Find the distance traveled by the ship.
I am having a hard time even starting this problem. I tried drawing a 30 degree angle (using "North" as the terminal side and the 3 miles along the side that I drew going northeast). I thought I would use the Law of Sines or Cosines but I can't even begin the problem!
Thank you!
1 solutions

Answer 225133 by Fombitz(13828) About Me  on 2010-06-15 22:55:44 (Show Source):
You can put this solution on YOUR website!
Break up the ship's travel into x and y components.
3 miles at 60=(+3%2Acos%2860%29,3%2Asin%2860%29)=(1.5,2.598)
2 miles at 150=(2%2Acos%28150%29,2%2Asin%28150%29)=(-1.732,1.0)
At this point the ship's position is
(1.5-1.732,2.598+1.0)=(-0.232,3.598)
In order to return back the ship will have to travel 0.232 in the x, and -3.598 in the y. The total distance is
D%5E2=%280.232%29%5E2%2B%283.598%29%5E2
D=sqrt%2813%29=3.606
The total distance the ship travels is then,
+Dt=3%2B2%2BD=5%2Bsqrt%2813%29=8.606 miles


Square-cubic-other-roots/314712: square root 32x^3y^4
Simplify the radical, assume that all variables are nonnegative.
1 solutions

Answer 225132 by Fombitz(13828) About Me  on 2010-06-15 22:46:55 (Show Source):


Square-cubic-other-roots/314711: square root 5x-5=square root 3x+7
Please show work.
1 solutions

Answer 225131 by Fombitz(13828) About Me  on 2010-06-15 22:44:59 (Show Source):
You can put this solution on YOUR website!
+sqrt%285x-5%29=sqrt%283x%2B7%29
Square both sides.
+5x-5=3x%2B7
2x=12
highlight%28x=6%29


Coordinate-system/314686: graph:
y<2/3x-4
1 solutions

Answer 225129 by Fombitz(13828) About Me  on 2010-06-15 22:43:14 (Show Source):
You can put this solution on YOUR website!
First graph the line,
y=%282%2F3%29x-4
graph%28300%2C300%2C-5%2C5%2C-8%2C2%2C%282%2F3%29x-4%29
Now pick a point not on the line.
(0,0) is an easy choice.
Test the inequality.
0%3C%282%2F3%29%280%29-4
0%3C-4
False, so (0,0) is not in the solution region.
Shade the region that doesn't include (0,0).
Solved by pluggable solver: Plot Any Inequality
Graphing function y%3C%282%2F3%29x-4:

graph%28+300%2C+300%2C+-5%2C+5%2C+-8%2C+2%2C+y%3C%282%2F3%29x-4+%29



test/314671: 3(absolute sign)4x + 5 (absolute sign) +5 < 14

Solve the inequality. Write the solution set in interval notation
1 solutions

Answer 225035 by Fombitz(13828) About Me  on 2010-06-15 16:31:42 (Show Source):
You can put this solution on YOUR website!
+3%2Aabs%284x+%2B+5%29+%2B5+%3C+14
+3%2Aabs%284x+%2B+5%29+%3C9
abs%284x%2B5%29%3C3
%284x%2B5%29%3C3 and -%284x%2B5%29%3C3
4x%3C-2 and 4x%2B5%3E-3
x%3C-1%2F2 and 4x%3E-8
x%3C-1%2F2 and x%3E-2
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.
.
(-2,-1%2F2)


Geometry_Word_Problems/314675: if the area a of a triangle is 60sq m and the base b is 20m what is the altitude h
1 solutions

Answer 225034 by Fombitz(13828) About Me  on 2010-06-15 16:27:50 (Show Source):
You can put this solution on YOUR website!
A=%281%2F2%29bh
60=%281%2F2%29%2820%29h
h=6
The height is 6 meters.


Quadratic-relations-and-conic-sections/314676: Find the coordinates of the point halfway between (3,4) and (-2,5)
1 solutions

Answer 225033 by Fombitz(13828) About Me  on 2010-06-15 16:27:03 (Show Source):
You can put this solution on YOUR website!
Use the midpoint formula,
xm=%28x1%2Bx2%29%2F2=%283-2%29%2F2=1%2F2
ym=%28y1%2By2%29%2F2=%284%2B5%29%2F2=9%2F2
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(1%2F2,9%2F2)


absolute-value/314534: 4|-6x + 6| + -3 = 93
1 solutions

Answer 225032 by Fombitz(13828) About Me  on 2010-06-15 16:25:52 (Show Source):


test/314670: (x + 2)^2/3 + 3(x + 2)^1/3 - 10 = 0
1 solutions

Answer 225030 by Fombitz(13828) About Me  on 2010-06-15 16:23:30 (Show Source):
You can put this solution on YOUR website!
Substitute first.
Let u=%28x%2B2%29%5E%281%2F3%29, then
u%5E2=%28x%2B2%29%5E%282%2F3%29
%28x%2B2%29%5E%282%2F3%29%2B3%28x%2B2%29%5E%281%2F3%29-10=0
u%5E2%2B3u-10=0
%28u%2B5%29%28u-2%29=0
Two "u" solutions:
u%2B5=0
u=-5
%28x%2B2%29%5E%281%2F3%29=-5
x%2B2=-125
x=-127
Not a valid solution since (-127)^(2/3) is undefined.
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u-2=0
u=2
%28x%2B2%29%5E%281%2F3%29=2
x%2B2=8
x=6



test/314663: 36x^4 - 85x^2 + 49 = 0
1 solutions

Answer 225028 by Fombitz(13828) About Me  on 2010-06-15 16:14:20 (Show Source):
You can put this solution on YOUR website!
Let u=x%5E2, then u%5E2=x%5E4,
36x%5E4+-+85x%5E2+%2B+49+=+0+
36u%5E2-85u%2B49=0
You can factor,
%2836u-49%29%28u-1%29=0
Two "u" solutions:
36u-49=0%0D%0A%7B%7B%7B36u=49
u=49%2F36
x%5E2=49%2F36
x=0+%2B-+7%2F6
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u-1=0
u=1
x%5E2=1
x=0+%2B-+1
You then have 4 "x" solutions.


Geometry_proofs/314662: What is the p and the q in If-Then statements,and in postulates?
1 solutions

Answer 225026 by Fombitz(13828) About Me  on 2010-06-15 16:08:43 (Show Source):
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p and q are variables that can have the value of TRUE or FALSE.
As examples,
p:The sun is in the sky.
q:5>0
r:The Celtics beat the Lakers.
s:Jim is smart.
t:The vuvzelas at the World Cup games are annoying.
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They take the place of the actual statements like x and y in algebraic expressions so that you can apply math logic rules without having to lug around entire statements.


Quadratic_Equations/314639: x square root + 25 x + 25 =9
1 solutions

Answer 225022 by Fombitz(13828) About Me  on 2010-06-15 16:01:24 (Show Source):
You can put this solution on YOUR website!
Is this the equation?
sqrt%28x%29%2B25x%2B25=9
or do you mean like this?
x%5E2%2B25x%2B25=9